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Proof step 158 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, min(n1, n2) + n4 = n1 + n5, LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, # buf0 < LEB_SIZE, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 < # buf, n3 + n2 < # buf, n < # buf3, n < # subarray(buf, 0, n3) + #(subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4)), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), n1 + n3 ≤ # buf + n0, min(n1, n2) ≤ n1 + n5, n3 ≤ # buf3, min(n1, n2) ≤ EB_PAGE_SIZE ⊦ (n < # subarray(buf, 0, n3) ⊃ subarray(buf, 0, n3)[n] ;(subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4) )[n - # subarray(buf, 0, n3) ] ) = (subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5))[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 159:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, min(n1, n2) + n4 = n1 + n5, LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, # buf0 < LEB_SIZE, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 < # buf, n3 + n2 < # buf, n < # buf3, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), n1 + n3 ≤ # buf + n0, min(n1, n2) ≤ n1 + n5, n3 ≤ # buf3, min(n1, n2) ≤ EB_PAGE_SIZE ⊦ (n < n3 ⊃ buf[n] ;(subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4))[n - n3] ) = (subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5))[n]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # subarray(buf, m, n) = n; (s)